Jerrica is packing a box that can hold at most 65 pounds. She starts by putting a container in the box that weighs 26 pounds. She plans to fill the rest of the box with books. Each book she places in the box weighs 1.3 pounds. Write an inequality for the number of books Jerrica can put in the box, and describe the solutions.(2 points)

Question

___x+___ ≤___, where x is the number of books Jerrica can put in the box. Jerrica can put at most ___  books in the box.

Answer 1

To set up the inequality for the number of books Jerrica can put in the box, we start with the weight limit of the box and subtract the weight of the container.

The container weighs 26 pounds, so the weight left for the books is:

\[ 65 - 26 = 39 \text{ pounds} \]

Each book weighs 1.3 pounds, so if \( x \) represents the number of books, the total weight of the books can be expressed as:

\[ 1.3x \]

The inequality that represents the maximum weight the box can hold is:

\[ 26 + 1.3x \leq 65 \]

Subtracting 26 from both sides gives:

\[ 1.3x \leq 39 \]

Now we can express this in the desired format:

\[ 1.3x \leq 39 \]

To find the maximum number of books \( x \), we divide both sides by 1.3:

\[ x \leq \frac{39}{1.3} \]

Calculating \( \frac{39}{1.3} \):

\[ \frac{39}{1.3} = 30 \]

Thus, Jerrica can put at most 30 books in the box.

So your complete answer would be:

\[ 1.3x \leq 39, \text{ where } x \text{ is the number of books Jerrica can put in the box. Jerrica can put at most } 30 \text{ books in the box.} \]